Algebra Examples

$\frac{5}{3} - 2 d = \frac{5}{6} d - d + 3$

Step 1

Since $d$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$\frac{5}{6} d - d + 3 = \frac{5}{3} - 2 d$

Step 2

Simplify $\frac{5}{6} d - d + 3$ .

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Step 2.1

Combine $\frac{5}{6}$ and $d$ .

$\frac{5 d}{6} - d + 3 = \frac{5}{3} - 2 d$

Step 2.2

To write $- d$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$\frac{5 d}{6} - d \cdot \frac{6}{6} + 3 = \frac{5}{3} - 2 d$

Step 2.3

Simplify terms.

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Step 2.3.1

Combine $- d$ and $\frac{6}{6}$ .

$\frac{5 d}{6} + \frac{- d \cdot 6}{6} + 3 = \frac{5}{3} - 2 d$

Step 2.3.2

Combine the numerators over the common denominator.

$\frac{5 d - d \cdot 6}{6} + 3 = \frac{5}{3} - 2 d$

Step 2.4

Simplify each term.

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Step 2.4.1

Simplify the numerator.

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Step 2.4.1.1

Factor $d$ out of $5 d - d \cdot 6$ .

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Step 2.4.1.1.1

Factor $d$ out of $5 d$ .

$\frac{d \cdot 5 - d \cdot 6}{6} + 3 = \frac{5}{3} - 2 d$

Step 2.4.1.1.2

Factor $d$ out of $- d \cdot 6$ .

$\frac{d \cdot 5 + d (- 1 \cdot 6)}{6} + 3 = \frac{5}{3} - 2 d$

Step 2.4.1.1.3

Factor $d$ out of $d \cdot 5 + d (- 1 \cdot 6)$ .

$\frac{d (5 - 1 \cdot 6)}{6} + 3 = \frac{5}{3} - 2 d$

Step 2.4.1.2

Multiply $- 1$ by $6$ .

$\frac{d (5 - 6)}{6} + 3 = \frac{5}{3} - 2 d$

Step 2.4.1.3

Subtract $6$ from $5$ .

$\frac{d \cdot - 1}{6} + 3 = \frac{5}{3} - 2 d$

Step 2.4.2

Move $- 1$ to the left of $d$ .

$\frac{- 1 \cdot d}{6} + 3 = \frac{5}{3} - 2 d$

Step 2.4.3

Move the negative in front of the fraction.

$- \frac{d}{6} + 3 = \frac{5}{3} - 2 d$

Step 3

Move all terms containing $d$ to the left side of the equation.

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Step 3.1

Add $2 d$ to both sides of the equation.

$- \frac{d}{6} + 3 + 2 d = \frac{5}{3}$

Step 3.2

To write $2 d$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$- \frac{d}{6} + 2 d \cdot \frac{6}{6} + 3 = \frac{5}{3}$

Step 3.3

Combine $2 d$ and $\frac{6}{6}$ .

$- \frac{d}{6} + \frac{2 d \cdot 6}{6} + 3 = \frac{5}{3}$

Step 3.4

Combine the numerators over the common denominator.

$\frac{- d + 2 d \cdot 6}{6} + 3 = \frac{5}{3}$

Step 3.5

Simplify each term.

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Step 3.5.1

Simplify the numerator.

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Step 3.5.1.1

Factor $d$ out of $- d + 2 d \cdot 6$ .

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Step 3.5.1.1.1

Factor $d$ out of $- d$ .

$\frac{d \cdot - 1 + 2 d \cdot 6}{6} + 3 = \frac{5}{3}$

Step 3.5.1.1.2

Factor $d$ out of $2 d \cdot 6$ .

$\frac{d \cdot - 1 + d (2 \cdot 6)}{6} + 3 = \frac{5}{3}$

Step 3.5.1.1.3

Factor $d$ out of $d \cdot - 1 + d (2 \cdot 6)$ .

$\frac{d (- 1 + 2 \cdot 6)}{6} + 3 = \frac{5}{3}$

Step 3.5.1.2

Multiply $2$ by $6$ .

$\frac{d (- 1 + 12)}{6} + 3 = \frac{5}{3}$

Step 3.5.1.3

Add $- 1$ and $12$ .

$\frac{d \cdot 11}{6} + 3 = \frac{5}{3}$

Step 3.5.2

Move $11$ to the left of $d$ .

$\frac{11 d}{6} + 3 = \frac{5}{3}$

Step 4

Move all terms not containing $d$ to the right side of the equation.

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Step 4.1

Subtract $3$ from both sides of the equation.

$\frac{11 d}{6} = \frac{5}{3} - 3$

Step 4.2

To write $- 3$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{11 d}{6} = \frac{5}{3} - 3 \cdot \frac{3}{3}$

Step 4.3

Combine $- 3$ and $\frac{3}{3}$ .

$\frac{11 d}{6} = \frac{5}{3} + \frac{- 3 \cdot 3}{3}$

Step 4.4

Combine the numerators over the common denominator.

$\frac{11 d}{6} = \frac{5 - 3 \cdot 3}{3}$

Step 4.5

Simplify the numerator.

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Step 4.5.1

Multiply $- 3$ by $3$ .

$\frac{11 d}{6} = \frac{5 - 9}{3}$

Step 4.5.2

Subtract $9$ from $5$ .

$\frac{11 d}{6} = \frac{- 4}{3}$

Step 4.6

Move the negative in front of the fraction.

$\frac{11 d}{6} = - \frac{4}{3}$

Step 5

Multiply both sides of the equation by $\frac{6}{11}$ .

$\frac{6}{11} \cdot \frac{11 d}{6} = \frac{6}{11} (- \frac{4}{3})$

Step 6

Simplify both sides of the equation.

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Step 6.1

Simplify the left side.

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Step 6.1.1

Simplify $\frac{6}{11} \cdot \frac{11 d}{6}$ .

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Step 6.1.1.1

Cancel the common factor of $6$ .

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Step 6.1.1.1.1

Cancel the common factor.

$\frac{6}{11} \cdot \frac{11 d}{6} = \frac{6}{11} (- \frac{4}{3})$

Step 6.1.1.1.2

Rewrite the expression.

$\frac{1}{11} (11 d) = \frac{6}{11} (- \frac{4}{3})$

Step 6.1.1.2

Cancel the common factor of $11$ .

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Step 6.1.1.2.1

Factor $11$ out of $11 d$ .

$\frac{1}{11} (11 (d)) = \frac{6}{11} (- \frac{4}{3})$

Step 6.1.1.2.2

Cancel the common factor.

$\frac{1}{11} (11 d) = \frac{6}{11} (- \frac{4}{3})$

Step 6.1.1.2.3

Rewrite the expression.

$d = \frac{6}{11} (- \frac{4}{3})$

Step 6.2

Simplify the right side.

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Step 6.2.1

Simplify $\frac{6}{11} (- \frac{4}{3})$ .

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Step 6.2.1.1

Cancel the common factor of $3$ .

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Step 6.2.1.1.1

Move the leading negative in $- \frac{4}{3}$ into the numerator.

$d = \frac{6}{11} \cdot \frac{- 4}{3}$

Step 6.2.1.1.2

Factor $3$ out of $6$ .

$d = \frac{3 (2)}{11} \cdot \frac{- 4}{3}$

Step 6.2.1.1.3

Cancel the common factor.

$d = \frac{3 \cdot 2}{11} \cdot \frac{- 4}{3}$

Step 6.2.1.1.4

Rewrite the expression.

$d = \frac{2}{11} \cdot - 4$

Step 6.2.1.2

Combine $\frac{2}{11}$ and $- 4$ .

$d = \frac{2 \cdot - 4}{11}$

Step 6.2.1.3

Simplify the expression.

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Step 6.2.1.3.1

Multiply $2$ by $- 4$ .

$d = \frac{- 8}{11}$

Step 6.2.1.3.2

Move the negative in front of the fraction.

$d = - \frac{8}{11}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$d = - \frac{8}{11}$

Decimal Form:

$d = - 0.\overline{72}$